IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

aks_0123456

`Q1 The tangents drawn from origin to circle x^2 + y^2 -2rx -2hy +h^2=0 are perpendicular iff:`

`Q2 If P(2,8) is an interior point of circle x^2 + y^2 -2x +4y -p=0 then set of P is:::`

`Q3 The number of integral values of @ for which x^2 + y^2 +@x +(1-@)y +5=0 is the equation of circle whose radius cannot exceed 5 is::`

sachinguptaiit

Radius of given circle

sachinguptaiit

Tangents drawn from origin can be perpendicular iff

coordinated of centre are of type (r,r)

hence h = r is the condition.

heavensablaze

hey aks is the answer for Q3 =10values? Plz reply

aks_0123456

nops...........sachin has solved it correctly..........16 is the answer........

allamraju

2)For a point (x₀,y₀) to lie in the interior of S,the conditon is S₀₀<0.

So,In this case,S₀₀=4+64-4+32-p<0

96-p<0 (or) p>96.

ankurgupta91

sry bt sachin has done it totally wrng
only the answer is cmng rght
nw see this

centre is ( -a/2 , (a-1)/2 )
radius <5
so, a^2/4 + (a-1)^2 / 4 -5 < =25

2a^2 - 2a - 119 < =0

a belongs to ( [1- sqrt(229) ]/ 2 , [1+sqrt(229)]/ 2 )
so, integral values that "a" can take are -7,-6,-5........7,8

so in total 16
thats the answer
hope u gt it ......

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Q1 The tangents drawn from origin to circle x^2 + y^2 -2rx -2hy +h^2=0 are perpendicular iff:

Q2 If P(2,8) is an interior point of circle x^2 + y^2 -2x +4y -p=0 then set of P is:::

Q3 The number of integral values of @ for which x^2 + y^2 +@x +(1-@)y +5=0 is the equation of circle whose radius cannot exceed 5 is::